This is pretty much what I suspect, but don't know for sure and thus why I'm asking.... ;)

Likewise, Windows keeps a cache of MAC addresses too, which you can see by running "arp -a" at the command prompt.

So as long as both devices are on the same switch and have established communication at least once with eachother, they'll both have knowledge of eachother via MAC address. Remember, your switch is running at Layer 2 of the OSI model. It has no knowledge of IP addressing. It should only go back to the router when it doesn't know where to go (DNS requests, Internet access, machines outside the local switch, etc).

They communicate directly. End of story. Run a speed test and you will see.
Ethernet is just a transport. It can run all sorts of protocols. You are running IP protocol, designed to find the shortest route. DHCP (Dynamic host configuration protocol) only exists to assign IP addresses to devices to make sure they do not conflict with other devices. Once you have an IP address you never talk to DHCP again, even if it drops your IP and gives it away. Routers only route traffic that needs to pass through it. Like your internet.

In a home network with more than one switch is it correct to assume that devices on the same switch will talk directly to each other or does the info still need to travel to the DHCP device (router) first and then back to the switch?

Here's the scenario... network switch on the remote side of a powerline Ethernet with PC(s) and home theater devices plugged directly into the switch... will the amp be able to access media from the PC directly through the switch, or would it still be depending on the powerline throughput?

Short answer - yes, if they're on the same switch they will talk directly to each other with your setup. Assuming a L2, unmanaged switch.

Specify IP's manually on the devices you are concerned about and reference the IP's not hostname when loading data.

If you DO NOT specify an IP when the DHCP lease is released the leasing agent will assign its self some arbitrary IP like 169.254.x.x (depending on the drivers the leasing agent may also automatically self assign when broadcasts are no longer being received from the DHCP server)